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By F. L. Vogel

Densities and distributions of dislocations in plastically bent germanium crystals before and after annealing were studied. In the bent and annealed crystals, the theoretical relationship between radius of curvature and density of dislocations is confirmed. Before annealing, however, more dislocations are present than required, and these are distributed with a minimum at the neutral axis and maxima at the top and bottom surfaces. On annealing, three significant changes occur in the bent bars: 1) the average dislocation density is reduced, presumably by the annihilation of opposite signs; 2) dislocations migrate from the high density outside regions toward the low density neutral axis, thus producing the equilibrium distribution of dislocations; and 3) a polygonized structure is formed by movement of the dislocations into walls normal to the slip plane. ETCHING to reveal edge dislocations'-" offers a unique opportunity to study, in germanium single crystals, the functioning of dislocations in plastic deformation. Plastic bending is ideally suited to this purpose because it produces a static array of edge dislocations in an ideally plastic material which is predictable from the theory." " Nye" has given a rather complete treatment of the geometry of bent crystals in terms of dislocations. The density of excess dislocations is related to the radius of curvature of the slip plane of a bent crystal, as shown in Fig. 1, assuming the absence of macroscopic elastic stresses. The curvature of any plane in the zone of the bend axis is found by resolving the Burgers vector into that plane, so that for the usual case where the slip plane is inclined at some angle 0 to the neutral plane of the bar, the equation applies, with T equal to the radius of curvature of the neutral plane of the bent crystal. Two predictions which are relevant to this study may be made from Eq. 1. First, in crystals bent to various radii, the average excess dislocation density is inversely proportional to the radius and second, for a bar bent to a radius which is large compared with its thick-

Jan 1, 1957

By V. J. Decarlo, J. J. Gilman

POLISHING pure zinc differs somewhat from polishing less reactive metals. The problem is not that of finding a suitable reagent, but rather of producing the polish in such a way that the surface remains polished after it is removed from the polishing bath. In other words., the anodic film that is vital to the polishing mechanism' must be tightly adherent and nonporous. It is usually desirable that it be thin. Polishing solutions consist of proper proportions of an acid and a strong oxidizing agent. In electro-polishing, the external circuit acts as the oxidizing agent. The proportions are critical because the essential surface film must be maintained at approximately constant thickness during the polishing process. In the case of zinc, chiefly two oxidizing agents, chromic and nitric acids, have been used. The simplest polishing reagent is concentrated nitric acid. However, it has certain disadvantages. It tends to pit: an excessive amount of heat is evolved during polishing; and the oxide film that it produces is not very stable, so that the polished sur-

Jan 1, 1957

By F. W. Jessen, James N. Howell

INTRODUCTION The determination of cloud points has to date been limited to rather transparent oils, visual observation of the formation of a solid phase being the criterion for the standard ASTM D 97-47 method. The need for a quiclc and simple method for determining cloud points under dynamic conditions for opaque crude oils became necessary in a study of fundamental aspects of paraffin deposition from crude oils. PREVIOUS WORK The determination of cloud points in opaque oils by viscosity temperature curves is fairly new, Young' described a method employing the capillary tube principle. No information exists relative to the determination of cloud points of crude or refined oils under dynamic conditions. Shock' noticed that deposition of paraffin from crude oils took place at temperatures at or below the temperature at which a sharp inflection point occurred in the viscosity-temperature curve. This observation indicates a possible correlation between this temperature and the cloud point of the crude oil. Reistle and Vietti1 have reported that when crude oils containing small amounts of asphaltic materials were heated to temperatures sufficiently high to solubilize these materials and immediately cooled the pour point of the crude oil was lowered as much as 70°F. Sachanen\ asribes this effect to the action of colloidal asphaltenes in preventing the formation of the crystalline structure necessary to maintain the oil in a rigid state. At high temperatures, asphaltenes are peptized, and the paraffin crystals formed at these temperatures adsorb the colloidal asphaltenes on their surface thereby hindering further growth of the crystals. Reistle" found, however, that such heating and cooling of crude oils had no effect upon the cloud points. This latter work dealt with a crude oil of fixed composition, and the question immediately arises as to the effect of varying the concentration of asphaltic materials on the cloud point. APPARATUS AND PROCEDURE All viscosity measurements were made with a Bendix Ultra-Viscoson. The Bendix Ultra-Viscoson, which consists of a vibrating probe and an electronic computer. measures viscosity by exciting a thin alloy steel blade on the end of a probe by short electrical pulses in damped oscillation at 28 kilocycles. The blade vibrates longitudinally with an amplilude of less than 55 micron or 20 millionths of an inch. Energy to protlucc this excitation is generated in he computer and transferred to the probe through the connecting cable. The oscillating blade is magnetostric-tive, i.e., it is capable of transforming electrical energy to mechanical energy in the ultrasonic range. Ultrasonic waves are produced in the material surrounding the blade by the oscillating motion of the blade causing layers of the material to slip back and forth over one another at a known frequency. The electronic computer calculates the energy required to produce the sliding motion which is in turn proportional to the viscosity of the material. Actual values of viscosity times density (centi-poise X grams/cc) are indicated on the computer and a continuous D-C signal is provided which is fed into a type 153 Electronic Recorder (manufactured by Brown Instruments Div. of Minneapolis-Honeywell Regulator Co.) The liquid sample container was fabricated from a Lucite cylinder and jacketed by a Luicite water bath. Early experiments using glass and steel sample containers were not satisfactory. since the Ultra-Viscoson was apparently affected by the alterzltion of the magnetic fields surrounding the probe by stresses set LIP in the glass and steel as it cooled. The procedure for determining viscosity-temperature curves was relatively simple. The temperature ot the sample was raised sufficiently high to solubilize all paraffin and asphalts present. After heating, the oil sample was immediately transferred

Jan 1, 1957

By Stephen R. Wilson

This paper is one of a series published by the Bureau of Mines on the mineral resources of the Nation. It describes briefly the occurrence of sodium sulfate in Salt Lake and Tooele Counties, Utah, presents data on sampling, and describes ex-traction and refining raw material and a mining research project that has been conducted on the deposits. ACKNOWLEDGEMENTS Acknowledgments are given to the Tintic Standard Mining Co., Salt Lake City, Utah, and Bartlett Chemicals, Inc., New Orleans, La., for permission to use data obtained by the companies. The authors also acknowledge the courtesy of J. A. Marsh and H. K. Thurber, geologists and mining engineers, for permission to use information in reports prepared by them.

Jan 1, 1957

By Dwight K. Smith

A new pozzolanic composition has been developed for cementing oil wells where moderate to high temperatures prevail. This material is an entirely different concept to other oil well cementing materials, such as portland cements, cements containing additives, or liquid resins. Its characteristics are such that it is not, at present, recommended for use at temperatures less than 140º F. It can he either accelerated or retarded across a wide range of well conditions. This new cement is composed of a pozzolanic material, hydrated lime, and a chemical activator to give it early initial strength. This material can be used in wells from 6,000 to 18,000 or more feet where temperature conditions are similar to those along the Gulf Coast. This cement, when set, has no soluble portion subject to leaching or any compounds that should be attacked by sulfate waters or brines. For this reason, it should be permanent when placed adjacent to formations carrying any type of fluid. The compressive strengths in 24 hours are more than adequate for wells where temperatures are 140°F and higher. These values ore in excess of many other types of cementing composition presently in use in the field. This pozzolanic composition does not retrogress in strength at high temperatures as do some other types of cementing materials. The slurry weights of this material will vary slightly according to the specific gravity and water requirements of the pozzolnn itself. The materials covered herein will mix from 13.5 to 14.3 lb/gal, and will have a waiting-on-cement time comparable to other materials used under the same conditions. Economically speaking, this composition is less expensive than either portland cements or retarded cements presently being used under deep well conditions. INTRODUCTION Pozzolans are siliceous material which, though not cementitious in themselves, contain constituents which at ordinary temperatures will combine with lime in the presence of water to form compounds which have a low solubility and possess cementing properties. The use of pozzolanic materials dates back many hundreds of years and both the ancient Greeks and Romans were aware that certain volcanic deposits, if finely ground and mixed with lime and sand, yielded a mortar which possessed special properties. Generally, the early strengths of such materials were rather weak and were considered insufficient for modern commercial usages. Pozzolanic materials have been used extensively with portland cement in mass concrete to obtain special properties. In recent years, large quantities of certain pozzolanic materials have been used successfully admixed into portland cements for oil well cementing. Pozzolans, being reactive silicates, will combine with the free lime that is an inherent component of set portland cements and thereby. becomes cementitious themselves. POZZOLANS FOR OIL WELL CEMENTING There are many types of pozzolans, some of which are more reactive than others. The quality of the pozzoIan depends on the degree of reactivity, chemical composition, fineness, and other less well understood factors. Some of the more widely accepted pozzolans are those classified as fly ashes, while others are certain materials of volcanic origin. pozzolans which require large vol-

Jan 1, 1957

The mining activities on the North Mine leases have, over the years, followed the orebody from the shallower depths at the southern end of the lease as it continued northwards at progressively increasing depths.Commencing from the south end, in the early days small shafts were used to obtain access to the orebody at the moderate depths involved.

Jan 1, 1957

The paper by Professors Sun and Mitchell illustrates the value of ultrasonics as a tool for the mineral engineer. In particular, it opens up a number of possibilities to those interested in the field of comminution. The provision of desliming technique, which is thorough as well as rapid, is a distinct contribution, but the data of the paper suggest applications beyond desliming, in that the same treatments may be useful for size determination purposes. Fig. 1 shows that a marked dependence exists between particle size and the height to which it can be elevated by ultrasonic vibrations. While the curves are only extended down to a size of about 100 p, the fact that they appear to be increasing in slope in this range suggests that the separation may be even more marked here. This, we feel, is very strong evidence that a method for fine sizing could be developed to use ultra- sonic waves as the separating force.

Jan 1, 1957

The first metal-mine accident-prevention course was prepared and published 1942-45 as a series of seven miners' circulars (Nos. 51-57). The course has been broadened, revised, and brought up to date and is being published as a similar series of seven miners' circulars on accident prevention at metal and nonmetallic mines. These circulars are: 1. Accident Statistics (Miners' Circular 51), dealing with general statistics on accidents and injuries at metal and nonmetallic mines, including causes, costs, and the uses of investigations and reports of all accidents.

Jan 1, 1957

By Nev A. Gokcen

DISCREPANCIES and scattering in the equilibrium data on the reactions of hydrogen, and CO with dissolved oxygen in liquid iron are un- duly large. Available experimental results on the reduction of liquid ferrous oxide, i.e., wüs-tite, with hydrogen and CO are questionable, as pointed Out by Darken and Gurry'l Direct determinations of the solubility of oxygen in liquid iron are subject to errors which cannot be easily reduced by further experimental refinements, and therefore an accurate but indirect method is highly desirable. The purpose of this investigation was, therefore, 1)

Jan 1, 1957

By W. L. Crentz

San Juan County, which occupies the extreme northwest corner of New Mexico, contains large reserves of coal in the Fruitland formation and in the Menefee formation of the Mesaverde group. The coals have bright luster, are brittle, and break easily in handling. All mines sampled are in the La Plata-Fruitland and Rio Chaco districts of the Durango-Gallup coal field. This large area, all within San Juan County, contains numerous coal beds 5 to 15 feet thick. Ellis2/ mentions the Carbonero (Fruitland in this report) bed in the La Plata-Fruitland district attaining a thickness of 36 feet. This bed has been correlated with the Carbonero bed, formerly mined at Carbon Junction, near Durango, Colo. During the field investigation covered by this report, no operating mine in the Fruitland bed was working a bed thickness of more than 15 feet.

Jan 1, 1957

By J. H. Keeler

The tensile characteristics of Zr-Fe binary alloys containing up to 5 atomic pet Fe are reported for the temperature range —195o to 500°C. A linear relation between stress at constant strain and volume fraction ZrFe2 was found. The coincidence of data from unalloyed zirconium with zero volume fraction ZrFe2 indicated little or no solid solution in IL-zirconium, in agreement with Hayes, Roberson, and O'Brien.' The absolute increase in strength due to particle strengthening, although decreasing with increasing temperature, was a greater percentage at high temperature. ZIRCONIUM is of interest for use in nuclear reactors because of its low neutron absorption, good corrosion resistance, and high melting temperature. The alloying of zirconium with iron has been considered as a means of increasing the mechanical strength of zirconium without seriously increasing the neutron absorption " over that of unalloyed zirconium. The Zr-Fe system has a eutectic at 934°C and 23.7 atomic pet Fe and a eutectoid at 800°C and 4.0 atomic pet Fe. The zirconium-rich end of this system determined by Hayes, Roberson, and O'Brien' is shown in Fig. 1. The intermetallic phase coexisting with a and ß-zirconium has been reported as Zr2Fe3,1 with a,, - 7.04A, and as ZrFe2,2 face-centered-cubic, the phase being of the MgCu, type (C-15). It was more recently agreed to be ZrFe33 and face-centered-cubic. This intermetallic phase is essentially insoluble in a-zirconium, the hexagonal-close-packed modification; and the lack of solubility makes the system particularly interesting metallurgically. The system is strengthened almost exclusively by particles of in-termetallic phase, and there is very little solid solution strengthening to complicate the analysis. The Bureau of Mines, in its survey of zirconium-base alloys,' reported the tensile properties of Zr-Fe alloys made from chloride process zirconium, induction melted in graphite crucibles, and swaged at 850°C in iron sheaths. Additional data on these ZrFe alloys were given by Hayes, Roberson, and O'Brien.' Chubb and Muehlenkamp% have recently reported the strength of Zr-Fe alloys containing up to about 1.25 atomic pet Fe. These alloys were made from crystal bar zirconium, hot worked at 820°C, annealed at 700°C, and tested both at room temperature and at 316°C. Experimental Procedure The materials used in this investigation were high purity zirconium made by the iodide process and electrolytic iron. The composition of the zirconium as obtained by spectrographic analysis and the nominal composition of the iron are given in Table I. Alloy ingots weighing 100 g were made by are-melting under argon in water-cooled copper crucibles in a multihearth furnace."

Jan 1, 1957

The authors of T.P. 4179 have conducted a large number of experimental water floods, and the data are reported in a very clear manner. These data show significant variations of residual oil saturation with changes in wettability, interfacial tension, flooding rate, and oil-water viscosity ratio. Furthermore, some of the data obtained cover a range of variables not previously reported in the literature. It is our opinion that at least some of the observed variation in oil recovery can be obtained only in floods made under conditions identical with those used by the authors. There are other systems which may be said to have the same wettability, but which exhibit an entirely different qualitative dependence of oil recovery on the experimental variables. In this regard, we would like to direct attention to several items which we feel are not given sufficient consideration in the paper. The first of these items has to do with wetting equilibrium. A survey of the current literature will reveal that little is known, and even less is understood, about wetting equilibrium. This is particularly true of the relation between contact angle measurements made under static conditions, and the wettability existing under the dynamic conditions of floods carried out at relatively high rates. We feel that this is a very important consideration, particularly in the floods the authors performed under what they consider to be "water-wet" conditions. It is our opinion that wetting equilibrium did not exist in these floods, except possibly at the very lowest rates. This opinion is in part based on some flooding tests we have made which are very similar to some of those described by the authors. These floods were made in unconsolidated cores, 6 in. long and 13/4 in. in diameter, made up of carefully graded glass spheres of the approximate size of the sand grains used in the subject paper. The cores were mounted vertically, and distilled water was used to displace a refined oil equivalent to the authors Soltrol C. The glass spheres had previously been carefully cleaned so that they were strongly wet by the water. The floods were made with and without an interstitial water saturation. When interstitial water was present, the solid surfaces were mostly covered with water prior to injecting the flooding phase. Consequently, a condition very near wetting equilibrium existed throughout the flood. The data in Fig. A show that under these eircumstances, rate had no influence on residual oil at flood-out, over the range of rates studied. On the other hand, in the absence of interstitial water, the surfaces are all covered with oil before the displacement. To achieve wetting equilibrium the injected water must displace the oil from the surfaces themselves. This is not a fast process. Therefore, the effective dynamic wetting condition in floods of this type must depend upon the flooding rate. When the flood rate is very low, compared to the rate at which wetting equilibrium is attained, the residual oil saturation at flood-out is essentially the same as the residual obtained when interstitial water is present. This is shown in Fig. A, and occurs because the dynamic wetting conditions are the same in both cases. However, at moderately high flooding rates, the rate has an important bearing on the amount of oil recovered because in this case the attainment of surface equilibrium is the slow step. We believe that, in the absence of an interstitial water saturation, oil recovery varies with rate because of the reasonably slow approach to wetting equilibrium which occurs during the displacement. In fact, as the rate is increased, the oil recovery performance indicates the core is becoming progressively less water-wet. At the highest rate there is even considerable simultaneous production of oil and water after breakthrough. This does not occur at the lower flooding rates, nor is there appreciable simultaneous oil and water produc-

Jan 1, 1957

By S. A. Braley

DRAINAGE water from coal mines is probably the most serious water pollution problem today, varying in importance according to location of the mines and geological structure. Drainage may be either acid or alkaline in character. Acid discharge, the most severely detrimental to a stream, is caused by natural oxidation of the sulfuritic material (FeS2) in the strata associated with the coal seam. Since the acid is the result of a natural reaction the acid water differs because it does not cease with abandonment of the mining operations. There is no known economical method of neutralizing acid mine water or any practical method to prevent oxidation of exposed pyrite. Since production of acid from a mine does not stop when mining stops, the total quantity produced depends entirely upon the excavated areas. The increasing volume of acid water in many mines has greatly increased operating costs. Pumping is expensive and acid mine waters are destructive of all equipment, especially metals in pumps and piping, and necessitate the use of corrosion-resistant materials. Discharge of the acid mine drainage into streams neutralizes their normal alkalinity, causes them to become acid, and produces an environment unfavorable for aquatic life and unsuited for industrial or domestic use without costly treatment.

Jan 1, 1957

By D. J. Carney, R. R. Burt, E. J. Whittenberger

Hardenability (multiplying) factors for carbon, mongonese, silicon, chromium, nickel, and molybdenum have been developed for hypereutectoid low-alloy steels in which bainite is the first subcritical transformation product. These factors permit the calculation of 95, 80, and 50 pct martensite hardenability from chemical composition when steels with spheroidized structures are quenched from 1475°, 1525°, and 1575°F. The strong contributions to hardenability of the less expensive elements, silicon and manganese, suggest their use to obtain additional hardenability in hypereutectoid low-alloy steels. DURING the past decade a number of investigators'"11 have carefully developed information which permits calculation of the hardenability of medium -carbon low-alloy steels from chemical composition and grain size. These data have been especially valuable in developing less costly low-alloy steel compositions with equivalent or Improved

Jan 1, 1957

By J. P. Powell

The importance of recovering more oil from known petroleum reserves has placed increasing emphasis on the application of secondary producing methods. One of the most successful of these has been the injection of water into depleted oil reservoirs. Water flooding is now recognized as a valuable conservation measure that not only prevents the premature abandonment of stripper leases but also is credited with reviving operations in many oil-producing areas previously abandoned. The injection of water into an oil-producing zone as a method of stimulating oil production was legalized in Kansas in 1935. Although water flooding had been attempted previously in other parts of the State, 1935 marked its introduction into the shallow stripper area of eastern Kansas. Two years later flooding was begun in the five-county area that is described in this report. Figure 1 is a map showing the water-flood areas in Allen, Bourbon, Crawford, Labette, and Neosho Counties, Kans. To July 1, 1955, the 77 projects in the oil fields of these 5 counties are credited with recovering an estimated 12.3 million barrels of oil that would not have been produced by methods used previously. These projects are expected ultimately to cover 10,700 acres, of which only 5,400 has been flooded to date.

Jan 1, 1957

By C. H. Samans, G. F. Tisinai, J. K. Stanley

The times at which the first detectable amount of a phase forms at temperatures between 900° and 1800°F were determined. Both X-ray diffraction and metallography were used to detect a in highly strained filings; metallography alone to detect it in annealed bulk samples of six different types of stainless steels. The a phase was found to form in accordance with the C-type reaction curve in both austenitic and ferritic alloys. In filings of types 304, 347, and 446, a formed in a few hours, and in types 316, 309, and 310, it formed in a matter of minutes at temperatures corresponding to the knee of the C-curve. Only in the bulk type 309 steel, after 500 hr, and in the bulk type 310 steel, after as short a time as 25 hr at temperature, was n detected; in both instances at approximately the same optimum temperature as in the filings. The annealing temperature affected a phase nucleation only for the filings of type 304 and 347 steels, and for the bulk samples of type 309 and 310 steels. KNOWLEDGE of both the rate of nucleation and the rate of growth of the new phase is required for a complete description of metallurgical rate phenomena. However, data on the time for nucleation alone may frequently be useful in evaluating the tendency of commercial stainlcss steels to form s under various conditions. Very little correlated information of this type is available in the literature. Shortsleeve and Nicholson' indicate that s forms in ferritic 24, 27 and 30 pet Cr steels according to a C-type of reaction curve, and Emmanuel's' data for austenitic type 310 steel also suggest this type of solid state reaction. In addition, significant, though fragmentary, information has been given by Binder, Dulis and Smith,4 Payson and Savage,.; Guarneri, Miller, and Vawter,8 rerichs and Clark,7 Wilder,5 Lismer, Pryce, and Andrews,' Smith, Dulis, and Link,10 Dulis, Smith, and Houston," and Henry, Cordovi, and Fischer." The bearing of these data on this work is covered in the discussion. The purpose of this paper is to present such correlated data on s formation in AISI type 304 (18 pct Cr-8 pet Ni), 347 (18 pet Cr-10 pet Ni-Cb), 316 (18 pet Cr-12 pet Ni-2 pet Mo), 309 (25 pet Cr-12 pet Ni), 310 (25 pet Cr-20 pet Ni), and 446 (27 pet Cr) stainless steels. Materials and Test Methods X-ray diffraction and metallographic methods were used to determine the first appearance of the s phase in cold worked filings and in annealed bulk samples of seven steels, under various combinations of time and temperature. The rate of growth of the s particles was not determined. Commercial heats of six AISI steels and a low carbon laboratory experimental heat containing about 28 pet Cr were studied. Analyses are given in Table I. Because cold work greatly accelerates the nucleation of s particles, the relative rates of s nucleation in mechanically strained samples, i.e., filings through 120 mesh, were determined for direct comparison with those in annealed bulk alloys of the same composition.

Jan 1, 1957

By L. M. Howe, J. Gordon Parr, E. Saarema

THE decreasing solid solubility limit at the titanium-rich end of the Ti-Cu constitutional diagram,' Fig. 1, suggests the possibility that titanium-rich alloys may be age-hardenable. However, results obtained by Holden et al. reproduced in Fig. 2 show that after quenching from 790°C the age-hardening of an alloy containing 1.7 pet Cu is very slight, while a 0.8 pet alloy decreases in hardness, during heat treatment at 400°C. It was believed possible that powder samples of alloys might show different results from the lump samples used by Holden et al., since small particles are often more sensitive to diffusion processes than larger samples. Consequently, a 1.9 pet (by weight) Cu alloy was made by the technique of levitation melting," checked for homogeneity, and filings of 48-65 Tyler screen size were cut from it for aging experiments. The filings were helium-quenched (by a technique described previously)' from 790°C, sealed in vacuo in silica tubes and aged at temperatures of 400°, 450°, and 500°C. Microscopic and X-ray examinations failed to reveal any structural changes during the aging process. This is not too surprising since early stages of precipitation do not usually manifest themselves in ways that are readily detectable by metallographic methods, and the extent of precipitation on overaging a 1.9 pet alloy is very small. However, hardness readings (taken on a Bergs-man micro hardness tester, using a 25 g load applied to a diamond indenter) do show a hardness peak at each aging temperature, Fig. 3. About a dozen readings were taken on each heat treated sample; the highest reading and the lowest reading were ignored and an average taken of the remaining values. In

Jan 1, 1957

By H. W. Paxton, C. C. Busby

IT has been shown previously' that strain aging can markedly improve the tensile properties of low carbon martensites, especially the yield-tensile ratio, without seriously affecting the ductility. In view of interest in high strength steels, an investigation has been made of the effect of strain aging following tension or rolling on the tensile properties of A1S1 4340 in an attempt to obtain a tensile

Jan 1, 1957

By Mary Barrett, Walter Rose

INTRODUCTION The conventional way to program reservoir problems* for solution on the electric analyzer1 is one which concentrates the block units towards the inner radius of the prototype system being represented by the analog model. This is achieved by the device of considering block units of equal value radial resistance, leading to the consequences: (1) the ratio of the external to the internal radius of each block unit is a constant (i.e. r1/ri-l = constant a); (2) the external radius of the nth block unit is equal to the innermost radius of the system times the constant a raised to the nth power: (3) the capacitance of the block units increase by a factor of a2 going out radially from the innermost to the outermost boundaries of the system; (4) given n block units in the radial direction, the capacitance ratio of the outermost to the innermost block unit is a (2n-2); and (5) the vertical resistance of the block units decrease by a factor of a going out radially from the innermost to the outermost boundaries of the system, such that the ratio of the maximum to minimum vertical resistance is also given by the factor a(2n-2) PRESENT PROGRAMMING METHOD While this conventional way of programming problems is quite adequate for routine uses of the electric analyzer, it leads to difficulties in those cases where the inner radius of the prototype system (e.g., the well-bore) is small compared to the external radius (e.g.. the external reservoir boundary). To handle such a case by the conventional method would require either that a large value be selected for the constant a or that a large number n, of radial block units be chosen. In consequence, the capacitance and vertical resistance ratios become impossibly large, as will be evident from the relations given above. In any event, the size of the smallest and largest capacitors will always be limited by the size of commercially available components, and the analyzer itself will determine how many mesh points are available for radial block units. For example, it can be shown that if the maximum capacitance ratio which can be electrically handled is a factor of l04, the maximum external radius of the system which can be considered (assuming an internal wellbore radius of 0.25 ft is: It is thus seen that in direct consequence of having the inner wellbore radius small compared to the external radius, models extending beyond 30 to 40 ft are not possible when the capacitance ratio is limited to l04. (NB. A value of 10-9 farads can perhaps be taken as the minimum electrical capacitance possible if corrections for the capacitance of the lead wires are to be avoided. Values greater than 10-5 farads would require the use of unstable and inaccurate electrolytic capacitors). On the other hand, models extending out to 500 to 5,000 ft may be desired in single-well problems, and hence the need for a revised method of problem programming. * REVISED PROGRAMMING METHOD The revised method of programming is one which attempts to retain the desirable features of the conventional method (viz. concentration of block units towards the inner boundary, simplicity in computation, etc.) without having as a consequence that impossible capacitance and vertical resistance ratios will be required. Other advantages will also be achieved by the revised

Jan 1, 1957

By R. M. Genevray, M. B. Bever, E. J. Suoninen

THE martensitic transformation in the ß-phase of the Cu-Zn system has been the subject of several investigations. The transformation is known to be reversible and to be affected by stress. Its temperature range has been determined as a function of composition. In the investigation reported here, the effect of tensile stresses on the transformation was investigated quantitatively. Some information was also obtained on the thermoelastic behavior of the martensite formed in the first stages of the transformation. Most of the experiments were done with alloy E of an earlier investigation;' this alloy analyzed 60.49 pct Cu and 39.51 pet Zn by weight. The methods of shaping and heat treatment were also essentially the same as those previously used. The stress was applied to the specimen immersed in a cooling liquid. The transformation was followed by measuring the electrical resistance with a Kelvin bridge and the elongation with a cathetometer. Fig. 1 shows the M, temperature as a function of stress. Resistance and strain measurements gave essentially identical values. The results suggest a roughly linear relation between M. and in the range investigated, up to 12 kg s mm". At higher stresses, plastic deformation begins to interfere seriously with this relationship. The increase of M, with stress is consistent with published work on the effect of stress on the martensitic transformation. The slope of the curve, 4°C per kg mm ", is of the same order of magnitude as the corresponding value calculated for steel.' Fig. 1 also shows the difference, AM, between the temperature of 50 pct transformation on cooling, as measured by changes in length, and that of 50 pct reverse transformation on heating. This difference, which may be considered a measure of the hysteresis, increases with stress; the decrease at highest stresses is probably associated with plastic deformation. Preliminary work using only resistance measurements was done with an alloy containing 60.15 pct Cu and 39.79 pct Zn by weight. The results indicated higher values o-F M, in agreement with the known variation of M. with composition.' The effect of stress on M, (2°C per kg mm-') was of the same order of magnitude as that shown in Fig. 1 for composition E. An increase in hysteresis with stress was also found. The following experiment was made in order to investigate a partially transformed structure. A specimen of alloy E was cooled to — 85°C under a stress of 4.7 kg mm-'. Under these conditions, the martensitic transformation started but did not go to completion. The stress was then released and the specimen cooled to — 105°C. Fig. 2 shows the measured elongation c. The first change in the slope of the curve indicates the beginning of the transformation under stress. Removing the load at —85°C caused a decrease in length to the value corresponding to the elastic elongation of the parent phase resulting from the applied stress. Hence, the marten-site formed in the first part of the experiment apparently disappears completely and without hysteresis upon the release of the stress. The increase in length on further cooling indicates renewed formation of martensite. These conclusions are consistent with the concept of "thermoelastic" martensite," which has been confirmed by test." Acknowledgments The authors are greatly indebted to Professor M. Cohen for his advice and encouragement. They also thank F. Paxton for assistance. Thanks are due the American Brass Co. which supplied the alloys. References E. Kaminsky and G. V. Kurdjumov: Zhur. Tekhn. Fiziki SSSR (1936) 6, p. 984. A. B. Greninger and V. G. Mooradian: Trans. AIME (1938) 128, p. 337. "J. E. Reynolds, Jr. and M. B. Bever: Trans. AIME (1952) 194, p. 1065; Journal of Metals (October 1952). 'A. L. Titchener and M. B. Bever: Trai~s. AIME (1954) 200, p. 303; Journal of Metals (February 1954). " 3. A. Kulin, M. Cohen, and B. L. Averbach: Trans. AIME (1952) 194. p. 661; Journal of Metals (June 1952). "J. K. Pate1 and M. Cohen: Acta Metallurgica (1953) 1, p. 531. 'C. Crussard: Comptes Rendus (1953) 237, p. 1709. ' G. V. Kurdjumov: Zhur. Tekhn. Fiziki SSSR (1948) 18, p. 999. G. V. Kurdjumov and L. G. Khandros: Dokl Akad. Nouk. SSSR (1949) 66. p. 211.

Jan 1, 1957